1. QGP and Dynamics of Relativistic Heavy Ion Collisions Tetsufumi Hirano The University of Tokyo, Komaba Thermal Quantum Field Theories and Their Applications

2. OUTLINE Basic Checks – –Energy density – –Chemical and kinetic equilibrium Dynamics of Heavy Ion Collisions – –Elliptic Flow and Perfect Liquid!? – –Recent Results from Hydro models – –Some Comments on the Discovery Summary and Outlook My Charge: To interpret recent experimental data at RHIC experimental data at RHIC from a QGP fluid dynamics point of view

3. Physics of the QGP Matter governed by QCD, not QED High energy density/temperature frontier  Toward an ultimate matter (Maximum energy density/temperature) Understanding the origin of matter which evolves with our universe Reproduction of QGP in H.I.C.  Reproduction of early universe on the Earth

4. Quark Gluon Plasma Hadronization Nucleosynthesis History of the Universe ~ History of Matter QGP study Understanding early universe

5. Little Bang! Relativistic Heavy Ion Collider(2000-) RHIC as a time machine! 100 GeV per nucleon Au(197×100)+Au(197×100) Collision energy Multiple production (N~5000) Heat side view front view STAR

6. BASIC CHECKS

7. Basic Checks (I): Energy Density Bjorken energy density  : proper time y: rapidity R: effective transverse radius m T : transverse mass Bjorken(’83) observables

8. Critical Energy Density from Lattice Stolen from Karsch(PANIC05); Note that recent results seem to be T c ~190MeV

9. Centrality Dependence of Energy Density PHENIX(’05)  c from lattice Well above  c from lattice in central collision at RHIC, if assuming  =1fm/c.

10. CAVEATS (I) Just a necessary condition in the sense that temperature (or pressure) is not measured. How to estimate tau? If the system is thermalized, the actual energy density is larger due to pdV work. Boost invariant? Averaged over transverse area. Effect of thickness? How to estimate area? Gyulassy, Matsui(’84) Ruuskanen(’84)

11. Basic Checks (II): Chemical Eq. Two fitting parameters: T ch,  B direct Resonance decay

12. Amazing fit! T=177MeV,  B = 29 MeV Close to T c from lattice

13. CAVEATS (II) Even e + e - or pp data can be fitted well! See, e.g., Becattini&Heinz(’97) What is the meaning of fitting parameters? See, e.g., Rischke(’02),Koch(’03) Why so close to T c ?   No chemical eq. in hadron phase!?   Essentially dynamical problem! Expansion rate  Scattering rate (Process dependent) see, e.g., U.Heinz, nucl-th/0407067

14. Basic Checks (III): Radial Flow Spectrum for heavier particles is a good place to see radial flow. Blast wave model (thermal+boost) Driving force of flow  pressure gradient Inside: high pressure Outside: vacuum (p=0) Sollfrank et al.(’93)

15. Spectrum change is seen in AA! O.Barannikova, talk at QM05 Power law in pp & dAu Convex to Power law in Au+Au “Consistent” with thermal + boost picture Large pressure could be built up in AA collisions

16. CAVEATS (III) Not necessary to be thermalized completely – –Results from hadronic cascade models. How is radial flow generated dynamically? Finite radial flow even in pp collisions? – –(T,v T )~(140MeV,0.2) – –Is blast wave reliable quantitatively? Consistency? – –Chi square minimum located a different point for  and  Flow profile? Freezeout hypersurface? Sudden freezeout?

17. Basic Checks  Necessary Conditions to Study QGP at RHIC Energy density can be well above  c. – –Thermalized? “Temperature” can be extracted. – –Why freezeout happens so close to T c ? Pressure can be built up. – –Completely equilibrated? Importance of Systematic Study based on Dynamical Framework

18. Dynamics of Heavy Ion Collisions: Elliptic Flow and Perfect Liquid

19. Dynamics of Heavy Ion Collisions Time scale 10fm/c~10 -23 sec Temperature scale 100MeV~10 12 K Freezeout “Re-confinement” Expansion, cooling Thermalization First contact (two bunches of gluons)

20. Why Hydrodynamics? Static EoS from Lattice QCDEoS from Lattice QCD Finite T,  field theoryFinite T,  field theory Critical phenomenaCritical phenomena Chiral property of hadronChiral property of hadron Dynamic Phenomena in HIC Expansion, FlowExpansion, Flow Space-time evolution ofSpace-time evolution of thermodynamic variables thermodynamic variables Once one accepts local thermalization ansatz, life becomes very easy. Energy-momentum: Conserved number:

21. What is Elliptic Flow? How does the system respond to spatial anisotropy? Ollitrault (’92) Hydro behavior Spatial Anisotropy Momentum Anisotropy INPUT OUTPUT Interaction among produced particles dN/d   No secondary interaction 0 22 dN/d   0 22 2v22v2 x y 

22. QGP mixed hadron Anisotropy of energy density distribution  Anisotropy of “Momentum” distribution TH&Gyulassy(’06) Time Evolution of a QGP Fluid

23. Time Evolution of v 2 from a Parton Cascade Model b = 7.5fm generated through secondary collisions saturated in the early stage sensitive to cross section (~1/m.f.p.~1/viscosity) v 2 is Zhang et al.(’99)ideal hydro limit t(fm/c) v2v2 : Ideal hydro : strongly interacting system

24. Schematic Picture of Shear Viscosity See, e.g. Danielewicz&Gyulassy(’85) Assuming relativistic particles, Perfect fluid:   0 shear viscosity  0 Shear flow Smearing of flow Next time step

26. Basis of the Announcement PHENIX(’03)STAR(’02) Multiplicity dependence p T dependence and mass ordering Hydro results: Huovinen, Kolb, Heinz,… response = (output)/(input) “Hydro limit” It is found that they reproduce v 2 (p T ) data accidentally. T.Hirano and M.Gyulassy,Nucl.Phys.A769 (2006)71.

27. Recent Hydro Results from Our Group

28. Centrality Dependence of v 2 Discovery of “Large” v 2 at RHIC v 2 data are comparable with hydro results. Hadronic cascade cannot reproduce data. Note that, in v 2 data, there exists eccentricity fluctuation which is not considered in model calculations. Result from a hadronic cascade (JAM) (Courtesy of M.Isse) TH et al. (’06).

29. Pseudorapidity Dependence of v 2  =0  >0  <0 v 2 data are comparable with hydro results again around  =0 Not a QGP gas  sQGP Nevertheless, large discrepancy in forward/backward rapidity  See next slides TH(’02); TH and K.Tsuda(’02); TH et al. (’06). QGP only QGP+hadron

30. Hadron Gas Instead of Hadron Fluid QGP core A QGP fluid surrounded by hadronic gas QGP: Liquid (hydro picture) Hadron: Gas (particle picture) “Reynolds number” Matter proper part: (shear viscosity) (entropy density) big in Hadron small in QGP T.Hirano and M.Gyulassy,Nucl.Phys.A769 (2006)71. See also talk/poster by Nonaka

31. Importance of Hadronic “Corona” Boltzmann Eq. for hadrons instead of hydrodynamics Including viscosity through finite mean free path Suggesting rapid increase of entropy density Deconfinement makes hydro work at RHIC!?  Signal of QGP!? QGP only QGP+hadron fluids QGP fluid+hadron gas T.Hirano et al.,Phys.Lett.B636(2006)299.

32. QGP Liquid + Hadron Gas Picture Works Well Mass dependence is o.k. Note: First result was obtained by Teaney et al. 20-30% Centrality dependence is ok Large reduction from pure hydro in small multiplicity events T.Hirano et al.,Phys.Lett.B636(2006)299.

33. Some Comments on the Discovery

34. 1. Is mass ordering for v 2 (p T ) a signal of the perfect QGP fluid? Mass dependence is o.k. from hydro+cascade. 20-30% Proton Pion Mass ordering comes from rescattering effect. Interplay btw. radial and elliptic flows  Not a direct sign of the perfect QGP fluid

35. 2. Is viscosity really small in QGP? 1+1D Bjorken flow Bjorken(’83) Baym(’84)Hosoya,Kajantie(’85)Danielewicz,Gyulassy(’85)Gavin(’85)Akase et al.(’89)Kouno et al.(’90)… (Ideal) (Viscous)  : shear viscosity (MeV/fm 2 ), s : entropy density (1/fm 3 )  /s is a good dimensionless measure (in the natural unit) to see viscous effects. Shear viscosity is small in comparison with entropy density!

36. A Probable Scenario TH and Gyulassy (’06) ! Absolute value of viscosityIts ratio to entropy density Rapid increase of entropy density can make hydro work at RHIC. Deconfinement Signal?!  : shear viscosity, s : entropy density Kovtun,Son,Starinets(’05)

37. Digression (Dynamical) Viscosity  : ~1.0x10 -3 [Pa s] (Water 20 ℃ ) ~1.8x10 -5 [Pa s] (Air 20 ℃ ) Kinetic Viscosity  : ~1.0x10 -6 [m 2 /s] (Water 20 ℃ ) ~1.5x10 -5 [m 2 /s] (Air 20 ℃ ) [Pa] = [N/m 2 ] Non-relativistic Navier-Stokes eq. (a simple form) Neglecting external force and assuming incompressibility.  water >  air BUT water < air

38. 3. Is  /s enough? Reynolds number Iso, Mori, Namiki (’59) R>>1  Perfect fluid Need to solve viscous fluid dynamics in (3+1)D  Cool! But, tough!  Causality problem (talk by Kunihiro, talk/poster by Muroya) (1+1)D Bjorken solution

39. 4. Boltzmann at work?  ~ 15 *  pert ! Caveat 1: Where is the “dilute” approximation in Boltzmann simulation? Is ~0.1fm o.k. for the Boltzmann description? Caveat 2: Differential v 2 is tricky. dv 2 /dp T ~v 2 /. Difference of v 2 is amplified by the difference of. Caveat 3: Hadronization/Freezeout are different. 25-30%reduction Molnar&Gyulassy(’00)Molnar&Huovinen(’04) gluonicfluid

40. 5. Does v 2 (p T ) really tell us smallness of  /s in the QGP phase? Not a result from dynamical calculation, but a “fitting” to data. No QGP in the model  0 is not a initial time, but a freeze-out time.  s /  0 is not equal to  /s, but to 3  /4sT 0  0 (in 1+1D). Being smaller T 0 from p T dist.,  0 should be larger (~10fm/c). D.Teaney(’03)

41. 6. Is there model dependence in hydro calculations? Novel initial conditions from Color Glass Condensate lead to large eccentricity. For CGC, see also talk/poster by Itakura Need viscosity even in QGP! Hirano and Nara(’04), Hirano et al.(’06) Kuhlman et al.(’06), Drescher et al.(’06)

42. Summary and Outlook We have discovered “something” really intriguing at RHIC We have discovered “something” really intriguing at RHIC –Perfect QGP fluid and dissipative hadron gas –Hydro at work as a signal of deconfinement(?) –Large cross section among partons is needed. Still a lot of work needed Still a lot of work needed –Initial stage, thermalization time, … –  and  /s are not sufficient to discuss viscous aspects in H.I.C. (“Perfect fluid” is a dynamic concept.) –Beyond Boltzmann/ideal hydro approach? –Success and challenge of hydrodynamics

44. Hadron Gas instead of Hadron Fluid 0 z t (Option) Color Glass Condensate sQGP core (Full 3D Hydro) HadronicCorona(Cascade,JAM)

45. Glauber-BGK and CGC Initial Conditions Which Clear the First Hurdle Glauber-BGK Glauber modelGlauber model N part :N coll = 85%:15% N part :N coll = 85%:15% CGC modelCGC model Matching I.C. via e(x,y,  ) Matching I.C. via e(x,y,  ) Centrality dependence Rapidity dependence CGC

46. p T Spectra for identified hadrons from QGP Hydro+Hadronic Cascade Caveat: Other components such as recombination and fragmentation should appear in the intermediate-high p T regions. dN/dy and dN/dp T are o.k. by hydro+cascade.

47. Results from Hydro + Cascade Glauber-BGKCGC

48. v 2 (p T ) from Hydro: Past, Present and Future 2000 (Heinz, Huovinen, Kolb…) Ideal hydro w/ chem.eq.hadrons 2002 (TH,Teaney,Kolb…) +Chemical freezeout 2002 (Teaney…) +Dissipation in hadron phase 2005 (BNL) “RHIC serves the perfect liquid.” 2004-2005 (TH,Gyulassy) Mechanism of v 2 (p T ) slope 2005-2006(TH,Heinz,Nara,…) +Color glass condensate Future “To be or not to be (consistent with hydro), that is THE question” -- anonymous -- anonymous History of differential elliptic flow ~History of development of hydro ~History of removing ambiguity in hydro 20-30% XXXXXXXXXXXXXX ????????????????? XXXXXXXXXXXXXX

49. Temperature Dependence of  /s We propose a possible scenario: Kovtun, Son, Starinets(‘05) Danielewicz&Gyulassy(’85) Shear Viscosity in Hadron Gas Assumption:  /s at T c in the sQGP is 1/4  No big jump in viscosity at T c !

50. Viscosity from a Kinetic Theory See, e.g. Danielewicz&Gyulassy(’85) For ultra-relativistic particles, the shear viscosity is Ideal hydro:   0 shear viscosity  0 Transport cross section

51. Schematic Picture of Shear Viscosity See, e.g. Danielewicz&Gyulassy(’85) Assuming relativistic particles, Perfect fluid:   0 shear viscosity  0 Shear flow Smearing of flow Next time step

52. A Long Long Time Ago… …we obtain the value R (Reynolds number)=1~10… Thus we may infer that the assumption of the perfect fluid is not so good as supposed by Landau.

53.  /s from Lattice A.Nakamura and S.Sakai,PRL94,072305(2005). Shear viscosity to entropy ratio from lattice (pure gauge) + an assumption of spectral function eta/s < 1 is one of the promising results of applicability for hydro at RHIC Challenging calculation! I love to see this region!!

54. Navier-Stokes Eq. and Relaxation Time Non-rela. (Cattaneo (’48))   0: Fourier law  : relaxation time Heat Eq. (Hyperbolic Eq.) Finite relaxation time Telegraph Eq.(Parabolic Eq.) Balance Eq. Constitutive Eq. Violation of causality cf.) 杉山勝、数理科学 (2002 年８月号）

55. Novel Viscous Fluid Dynamics How to get constitutive eqs.? 2 nd thermodynamic law Balance Eqs Constitutive Eq. Mueller,Israel,Stewart,… 1 st order2 nd order

56. Toward determination of transport coefficient of the QGP (Linear Response) ＝ (Transport Coefficient) x (Thermodynamic Force) bulk, shear, heat conductivity Lattice QCD + Kubo formula Relaxation for viscosity ： It can be obtain from a comp. btw. Boltzmann Eq. and visc. fluid dynamics.  Higher order moment for n(1±n) Can it be obtained from Lattice? Navier-Stokes eq. (1 st order) Novel rela. visc. fluid dynamics (2 nd order) Israel,Stewart Nakamura,Sakai

57. How Do Partons Get Longitudinal Momentum in Comoving System? Free Streaming eta=y dN/dy y dN/dy y Sum of delta function Width  “Thermal” fluctuation Sheet:eta=const

58. 2  2 Collisions Do Not Help! Xu and Greiner, hep-ph/0406278 Only 2  2 collisions, partons are still in a transverse sheet eta~y~const. 2  3 may help.

59.  /s from MD simulations Y.Akimura et al., nucl-th/0511019 eta/s has a minimum in the vicinity of T c ! No thermal qqbar production  Preliminary result

60. Statistical Model Fitting to ee&pp Becattini&Heinz(’97) Phase space dominance? “T” prop to E/N? See, e.g., Rischke(’02),Koch(’03)

61. Hadron phase below T ch in H.I.C. “chemically frozen”  Themalization can be maintained through elastic scattering. “chemically frozen”  Themalization can be maintained through elastic scattering. There still exit “quasi-elastic” collisions, e.g. There still exit “quasi-elastic” collisions, e.g. The numbers of short-lived resonances can be varied. (Acquirement of chemical potential) The numbers of short-lived resonances can be varied. (Acquirement of chemical potential) Recent data suggests importance of (process dependent) hadronic rescattering Recent data suggests importance of (process dependent) hadronic rescattering –Hard to describe this by hydro.

62. A Closer Look Reveals Details of Hadronic Matter Stolen from M.Bleicher (The Berkeley School)

63. How Reliable Quantitatively? Radial flow in pp collisions? central peripheral  Smallrescattering Systemexpands like this trajectory?